The Stacks project

Situation 70.6.1. Let $S$ be a scheme. Let $B = \mathop{\mathrm{lim}}\nolimits B_ i$ be a limit of a directed inverse system of algebraic spaces over $S$ with affine transition morphisms (Lemma 70.4.1). Let $0 \in I$ and let $f_0 : X_0 \to Y_0$ be a morphism of algebraic spaces over $B_0$. Assume $B_0$, $X_0$, $Y_0$ are quasi-compact and quasi-separated. Let $f_ i : X_ i \to Y_ i$ be the base change of $f_0$ to $B_ i$ and let $f : X \to Y$ be the base change of $f_0$ to $B$.

Comments (0)

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 084W. Beware of the difference between the letter 'O' and the digit '0'.



View Situation 70.6.1 as pdf